Title: Period proliferation in periodic states in cyclically sheared jammed solids

Abstract

Athermal disordered systems can display a remarkable response to an applied oscillatory shear: After a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study here the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.

@article{osti_1596538,
title = {Period proliferation in periodic states in cyclically sheared jammed solids},
author = {Lavrentovich, Maxim O. and Liu, Andrea J. and Nagel, Sidney R.},
abstractNote = {Athermal disordered systems can display a remarkable response to an applied oscillatory shear: After a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study here the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.},
doi = {10.1103/PhysRevE.96.020101},
journal = {Physical Review E},
number = 2,
volume = 96,
place = {United States},
year = {2017},
month = {8}
}

Here, we study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. In contrast to these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actuallymore » have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.« less

Here,more » at densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ Z , is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. Additionally, the second, ξ f , is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ f , the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ Z and ξ f are different and appear to be different in two and three dimensions.« less

Journal ArticleGoodrich, Carl P.
; Liu, Andrea J.
; Sethna, James P. - Proceedings of the National Academy of Sciences of the United States of America

Here, we propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yieldsmore » insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.« less